OSR: Teleport Spells (and also math)

Teleport spells in my game are very rare and very dangerous. Most wizards refuse to store them in their brains and use scrolls or wands instead. A teleport spell is convinced that two objects need to be switched. It exchanges them with a thunderclap of displaced air. The two objects have to be of approximately equal mass. Teleport spells sometimes get over-eager. If your fireballs spell gets excited you might get a headache or shoot flames from your nose. If a teleport spell gets excited, it might swap your brain (or part of it) with a nearby object. It's better to lose a scroll or a wand than your frontal lobes.

The latitude between the two objects also matters. We're going to use some approximations to make the math convenient. If you want to more precision, I'd have to ask "why?"

This might seem fiddly, but teleport spells are rare enough that the extra rules won't slow the game down. You can also eyeball results pretty easily.

Creation rotates at approximately 1000 miles per hour at the equator, decreasing by the cosine of your lattitude (in degrees) as you move away from the equator. (The equator is 0 degrees, the poles are 90 degrees). A parallel of latitude is about 72 miles. If you were on the equator and you walked 7 parallels north (504 miles), your rotational speed would decrease to (cosine(7)= 0.993, 0.993 x 1000 mph = 993 mph.) Conveniently, 72 miles is 12x 6 mile hexes.

Here's how the table works. Let's say you want to teleport one hex north. You are currently on the 20th parallel. If you moved all the way to the 21st parallel (12 hexes), you'd gain 6.1 miles per hour. But you are only moving one hex, so you gain (6.1/12) 0.5 miles per hour. That's a brisk tortoise pace, so air resistance cancels it out almost instantly. You arrive (or the object you swap with) arrives with a slight jolt.

Let's say you want to teleport from the 20th parallel to the 59th. Sum all the speed gain from the 21st to the 59th parallels to get 424.7 miles per hour. That's pretty quick. If you arrive at that speed, you'll fly through the air like a ragdoll and die. Air resistance will knock you unconscious. It's better to have the object you're swapping with take that speed (if you can fine-tune the spell). You'll arrive with a thump. It will arrive with a thunderclap, speed through the air, smack into something, and explode. The direction is due west (if moving closer to the equator) or due east (if moving further from it). I think. Someone check my math here.

As a general rule, you transfer 1d100% of your speed + 10% for every dice (or level) you invest in the spell + 10% for every time you've cast this particular teleport spell. 

For example, a wizard who invests 3 MD in a spell and has cast it twice before gets to transfer 1d00+50% of their speed to the swapped object.

Example Spells:

Royal Teleport
R: Creation T: 2 people or objects, 1 must be the caster D: instant
The caster, and any number of willing people or objects touching the caster, teleport to a designated location the caster has seen before or knows well enough to visualize. The spell swaps the caster, etc. with an equal mass of royalty from near the arrival area. If no royalty can be located, the spell fails. Dead royals, crowns, thrones, paintings, tapestries, archbishops, cardinals, and history books all count. Living royalty may Save to resist destiny. 

Blanchford's Aquatic Miracle
R: Creation T: 2 people or objects, 1 must be the caster D: instant
The caster, and any number of willing people or objects touching the caster, teleport to a designated location the caster has seen before or knows well enough to visualize. The location must be near water or underwater. The caster, etc. appear underwater, 1d10 meters down. The spell swaps them with an equal mass of water. Bear in mind that traveling quickly through water is much more dangerous than traveling quickly through air. Increase all damage by 1d6. Most wizards who use this spell wear specialized suits with hydrodynamic hats and pauldrons.

Parallel	Miles Between	Hexes Between	Mile Per Hour Gain	Cities (North)	Cities (South)
0	0	0	0
1	72	12	0.2	Nairobi
2	72	12	0.5
3	72	12	0.8
4	72	12	1.1
5	72	12	1.4
6	72	12	1.7
7	72	12	2.0
8	72	12	2.3
9	72	12	2.6
10	72	12	2.9
11	72	12	3.2
12	72	12	3.5
13	72	12	3.8	Bangkok
14	72	12	4.1	Guatemala City
15	72	12	4.4		Brasília
16	72	12	4.7
17	72	12	5.0
18	72	12	5.2
19	72	12	5.5	Mexico City
20	72	12	5.8
21	72	12	6.1	Honolulu
22	72	12	6.4		Rio de Janeiro
23	72	12	6.7
24	72	12	7.0
25	72	12	7.2
26	72	12	7.5		Johannesburg
27	72	12	7.8		Brisbane
28	72	12	8.1
29	72	12	8.3
30	72	12	8.6
31	72	12	8.9	Shanghai	Córdoba
32	72	12	9.1
33	72	12	9.4
34	72	12	9.6	Los Angeles	Buenos Aires
35	72	12	9.9	Kyoto	Canberra
36	72	12	10.1
37	72	12	10.4		Melbourne
38	72	12	10.6	Washington
39	72	12	10.9
40	72	12	11.1	New York City
41	72	12	11.3		Wellington
42	72	12	11.6	Rome
43	72	12	11.8
44	72	12	12.0	Minneapolis
45	72	12	12.2
46	72	12	12.4
47	72	12	12.7
48	72	12	12.9	Paris
49	72	12	13.1	Vancouver
50	72	12	13.3
51	72	12	13.5	London
52	72	12	13.7
53	72	12	13.8	Dublin
54	72	12	14.0		Ushuaia
55	72	12	14.2	Moscow
56	72	12	14.4
57	72	12	14.6	Inverness
58	72	12	14.7
59	72	12	14.9	Oslo
60	72	12	15.0
61	72	12	15.2
62	72	12	15.3
63	72	12	15.5	Trondheim
64	72	12	15.6
65	72	12	15.8
66	72	12	15.9
67	72	12	16.0
68	72	12	16.1	Inuvik
69	72	12	16.2
70	72	12	16.3
71	72	12	16.5
72	72	12	16.6
73	72	12	16.6
74	72	12	16.7
75	72	12	16.8
76	72	12	16.9
77	72	12	17.0
78	72	12	17.0
79	72	12	17.1
80	72	12	17.2
81	72	12	17.2
82	72	12	17.3
83	72	12	17.3
84	72	12	17.3
85	72	12	17.4
86	72	12	17.4
87	72	12	17.4
88	72	12	17.4
89	72	12	17.4
90	72	12	17.5

Speed	Example	Danger
0.1 mph	Snail Speed	None
0.5 mph	Fast Tortoise Speed	None
3 mph	Walking Pace	Save vs Dex or fall down (no damage)
5 mph	Brisk jog	Save vs Dex or fall down (1 damage)
10 mph	Running Speed	Save vs Dex or 1d4 damage.
25 mph	Sprint	Save vs Dex or 1d6 damage. Need at least 20' to slow down.
40 mph	Dangerous Sprint	Faster than you can run by your own power. Save vs Dex or 1d6 damage. Need at least 50' to slow down.
50 mph	Tumble	Cannot keep footing. 1d6 damage, prone, and stunned for 1 minute.
100 mph	Car Accident	No time to touch ground. 2d6 damage, prone, Save vs another 1d6 damage.
200 mph	Major Car Accident	4d6 damage, 1 fatal wound, and Save vs another 2d6 damage. You fly across the landscape.
More	Mangled	Probably dead. -10 HP, 1d6 fatal wounds.